Differential Properties of Information in Jump-diffusion Channels

2025-01-10

AI Summary

This study addresses the poorly understood information evolution dynamics in jump-diffusion channels. We propose a generalized jump-diffusion communication model that systematically characterizes the differential properties of entropy and mutual information. Methodologically, we extend the de Bruijn identity and the I-MMSE relationship—originally established for Gaussian diffusion—to general Markov processes for the first time, thereby establishing an information-theoretic differential analysis framework grounded in the Kramers–Moyal and Kolmogorov–Feller equations. Our key contributions include: (i) deriving an explicit differential expression for mutual information with respect to signal-to-noise ratio; (ii) unifying Fisher-type information measures and mismatched Kullback–Leibler divergence within a single analytical framework; and (iii) revealing the nonlinear coupling mechanism between jump and diffusion components in information transmission. These results provide a novel paradigm for information-theoretic modeling of non-Gaussian, discontinuous channels.

Technology Category

• Machine Learning: Information Theory
• Search and Optimization: Mixed Discrete/Continuous Search
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Web Mining and Content Analysis: Content-based information diffusion
• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks
• Security and Privacy: Large-scale security measurements

Abstract

We propose a channel modeling using jump-diffusion processes, and study the differential properties of entropy and mutual information. By utilizing the Kramers-Moyal and Kolmogorov-Feller equations, we express the mutual information between the input and the output in series and integral forms, presented by Fisher-type information and mismatched KL divergence. We extend de Bruijn's identity and the I-MMSE relation to encompass general Markov processes.

Problem

• Information Dynamics
• Fisher Information
• Diffusion Communication Model

Innovation

• Jump-Diffusion Communication Model
• Fisher Information
• Information Variability Analysis